The greatest increases in In due time MoneyGram separated from the Western Union and became an independent brand. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. In MoneyGram were added or converted new currencies in an additional 29 countries during the past year, providing consumers with a wide array of currency payout options. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes.